Contraction Rate and Its Relationship to Frontogenesis, the Lyapunov Exponent, Fluid Trapping, and Airstream Boundaries

Abstract

Although a kinematic framework for diagnosing frontogenesis exists in the form of the Petterssen frontogenesis function and its vector generalization, a similar framework for diagnosing airstream boundaries (e.g., drylines, lee troughs) has not been constructed. This paper presents such a framework, beginning with a kinematic expression for the rate of change of the separation vector between two adjacent air parcels. The maximum growth rate of the separation vector is called the instantaneous dilatation rate and its orientation is called the axis of dilatation. Similarly, a maximum decay rate is called the instantaneous contraction rate and its orientation is called the axis of contraction. These expressions are related to the vector frontogenesis function, in that the growth rate of the separation vector corresponds with the scalar frontogenesis function, and the rotation rate of the separation vector corresponds with the rotational component of the vector frontogenesis function.Because vorticity can rotate air-parcel pairs out of regions of deformation, the instantaneous dilatation and contraction rates and axes may not be appropriate diagnostics of airstream boundaries for fluid flows in general. Rather, the growth rate and orientation of an airstream boundary may correspond better to the so-called asymptotic contraction rate and the asymptotic axis of dilatation, respectively. Expressions for the asymptotic dilatation and contraction rates, as well as their orientations, the asymptotic dilatation and contraction axes, are derived. The asymptotic dilatation rate is related to the Lyapunov exponent for the flow. In addition, a fluid-trapping diagnostic is derived to distinguish among adjacent parcels being pulled apart, being pushed together, or trapped in an eddy. Finally, these diagnostics are applied to simple, idealized, steady-state flows and a nonsteady idealized vortex in nondivergent, diffluent flow to show their utility for determining the character of air-parcel trajectories and airstream boundaries.

Life Cycle and Mesoscale Frontal Structure of an Intermountain Cyclone

“…To limit pressure reduction artifacts, we use 1500-m pressure (calculated following Steenburgh and Blazek 2001) instead of sea level pressure since 1500 m is near the mean elevation of intermountain observing sites. Following Cohen and Kreitzberg (1997), we classify the GBCZ as an airstream boundary because it is a wind shift line separating two relatively distinct airstreams. Following Cohen and Kreitzberg (1997), we classify the GBCZ as an airstream boundary because it is a wind shift line separating two relatively distinct airstreams.…”

On the Poleward Motion of Midlatitude Cyclones in a Baroclinic Meandering Jet

“…In the case of slightly meandering jets, the Okubo-Weiss criterion is adequate while it is less adequate for flows with strong curvature (Lapeyre et al 1999;Rivi ere et al 2003). Note also that Cohen and Schultz (2005) have introduced this quantity to diagnose fronts or airstream boundaries in the troposphere. Figure 5 shows the effective deformation field D for the lower layer.…”

Kinematic and Moisture Characteristics of a Nonprecipitating Cold Front Observed during IHOP. Part I: Across-Front Structures

“…Boundary layer convergence zones (or boundaries) have long been known to be key factors in convection initiation and evolution (e.g., Byers and Braham 1949;Wilson and Schreiber 1986;Cohen and Kreitzberg 1997;Cohen and Schultz 2005). An examination of the literature suggests that boundaries such as gust fronts (e.g., Charba 1974;Wakimoto 1982;Weckwerth and Wakimoto 1992;Friedrich et al 2005), sea-breeze fronts (e.g., Blanchard and Lopez 1985;Atkins et al 1995;Fovell 2005), and drylines (e.g., Fujita 1970;Koch and McCarthy 1982;Schaefer 1986;Hane et al 1997;Murphey et al 2006) have received the largest amount of attention in terms of documenting their kinematic and moisture characteristics for convective weather forecasting applications.…”